Sure sounds like dry, hard soil to me. I am not familar with the tine design on that Landpride, but my Turfco tines pull a 3/4" diameter plug about 3"-3.5" long. When the tine comes around again during the tine wheel rotation, the last core carried in the tubular tine is pushed out (ejected) through an opening in the tine closer to the hub as the tine enters the soil and cuts a new plug. After a proper pass, you should have cores laying around everywhere as each new plug pulled has pushed the last plug out of the tine.
I noticed some differences in tines on core aerators when I was shopping. A properly designed coring tine is a smaller diameter on the business end where it enters the soil, and gradually a larger diameter as measured toward the hub and ejection slot or "window." I've heard these called spoons before, too, so maybe my terminology isn't quite accurate.
It's also important to get the unit oriented properly so the tines/spoons enter and exit the soil at the proper angle. A little tweaking with the toplink on most units can help cut nice clean plugs when the soil is moist enough. Of course soils that need aeration are the hardest to aerate /forums/images/graemlins/crazy.gif